Introduction

The response of a simple ice-sheet model forced by a periodic change in the climate point (the distance from the poleward limit of land to the point where snow persists at sea-level year-round) exhibits a bifurcation when certain dimensionless parameters undergo realistic changes. These dimensionless parameters are related to the poleward limit of continents as well as to the frequency of the climate point variation and other parameters. It is postulated that this bifurcation may be responsible for the initiation of large glacial cycles about 900 ka BP, following smaller, higher frequency ice-sheet advances and retreats before that time (Reference Watts and HayderWatts and Hayder 1983). It seems clear that the latitudinal locations of continents can affect the formation of ice sheets through interaction with the seasonal cycle.

We present here some results that we recently obtained with a two-dimensional, seasonal, diffusive, energy-balance climate model with a mixed-layer ocean and simple continents. The model itself has been discussed by Reference HayderHayder (unpublished) and Reference Watts and HayderWatts and Hayder (in press), and the interested reader is referred to those papers for details.

The results that we present here are mostly concerned with the effect on the model seasonal cycle of shifting land-sea distribution. The model was first run with the distribution shown in Figure 1. There is a cluster of continents located along 0° longitude. The land fraction shown corresponds closely to the present distribution of continents. Some representative seasonal data are shown in Figure 2 and Figure 3. Snow was assigned to land areas where the temperature was lower than −1°C and sea ice where the surface temperature over the sea was lower than −3.5°C. Model results are compared with the data of Reference Kukla and GribbinKukla (1978). Model parameters, such as diffusivities and albedos, are very near those in common use. Very little tuning of the model was necessary to produce an accurate seasonal cycle.

Fig. 1 The “present” land-sea distribution used in the model.

Fig. 2 Snowline extent in the northern hemisphere.

Fig. 3 Sea-ice extent in the southern hemisphere.

Next, we performed three experiments in which the model seasonal cycle was calculated for three different land fraction distributions. In the first case all the land is located in the southern hemisphere. The total land area is equal to the present area. Figure 4 shows the location of the snow and sea-ice limits as functions of season. The very large land fraction in the southern hemisphere leads to a very large seasonal cycle. Snow reaches 26°S latitude during the winter, but melts completely during midsummer. In Figure 5 the continent extends from the South Pole to the North Pole, but the land fraction in the southern hemisphere is still too large to permit snow to remain on the continent during the midsummer. With the land fraction distribution shown in Figure 6, the seasonal cycle has become so small that snow remains on the continent in the southern hemisphere during the entire year.

Fig. 4 Snowline extent in the southern hemisphere as generated by the model.

Fig. 5 Snowline extent in the southern hemisphere as generated by the model.

Fig. 6 Snowline extent in the southern hemisphere as generated by the model.

We first point out that these are quite obviously very simple preliminary experiments from which we can draw only broad conclusions. It has often been suggested (e.g. Reference BeatyBeaty 1978) that the formation of polar ice sheets requires large land masses at or near the poles. These experiments make it clear that this is a necessary condition, but not a sufficient one. If the land mass near the pole is too large, large seasonality does not permit the growth of ice sheets because the summers are too warm. It seems entirely possible that the absence of an Antarctic ice sheet before 30 to 50 Ma BP was at least partly due to the fact that the land mass near the South Pole was too large to permit snow to remain on the ground for the entire year.

Shifting continentatl distributions must surely have been accompanied by changes in the circulation of the ocean, and, therefore, changes in the poleward advection of heat (Reference Kvasov and VerbitskyKvasov and Verbitsky 1981). In its present form, our model cannot account for this. It is certainly an important effect, and we are now modifying our model in such a way that we can include it. It seems clear that one result of including an increased poleward advective heat flux by the oceans, as suggested by Reference Frakes, Kemp, Tarling and RuncornFrakes and Kemp (1973), will be to increase the annual average temperature on the continent near the South Pole. This is consistent with the belief that polar climates were warmer during the Cretaceous.

Finally, we emphasize our main point. While a land mass must be close to a pole in order for an ice sheet to form (Reference Watts and HayderWatts and Hayder 1983, Reference Watts and Hayderin press, Reference Oerlemans, Berger, Imbrie, Hays, Kukla and SaltzmanOerlemans in press) it seems possible for the land mass to be too large. (This is probably why the North American ice sheet formed before the Scandinavian ice sheet during the Quaternary ice age.) We conclude that a realistic model with which to study the initial formation of the Antarctic ice sheet 30 to 50 Ma BP should contain a land-sea distribution and a seasonal cycle, as well as realistic poleward advection by ocean currents.